tjeske, the terminology in my Netgear D6400 router "6to4 Tunnel" settings is "6to4."
Look carefully through the list of options. There exist 3 different but still quite similar tunnel protocols: 6to4, 6in4, and 6rd. Which of them does your router support? 6rd is the most flexible and if configured correctly can be made compatible with either 6in4 or 6to4.
What is the difference between "6in4" and "6to4"?
With 6to4 you get IPv6 addresses which are constructed from your IPv4 address. There is no provider as such, you will be relying on third party relays. You have little control over the choice of third party relays and consequently there isn't much you can do when they are unreliable.
With 6in4 you choose a tunnel provider (such as HE). Your traffic goes through your chosen provider and if it doesn't work you can contact your provider or choose a different provider.
There is also a hybrid between the two called 6rd. It has more configuration options and can be configured manually or autoconfigured through DHCP.
6to4 is a different tunnel protocol than 6in4. They are not compatible.
It's true that they are different and that a router configured with 6to4 is no use for communicating with HE. But they are still compatible enough that you can make 6to4 and 6in4 communicate directly with each other. I wouldn't recommend it though. Anything involving 6to4 should be recommended anymore.